Some of the tools you should have before you embark upon this chair making odyssey include:

Table saw

Band saw

Drill press

Jointer

Right angle grinder

Planer is not essential but is nice to have sometimes

Router(s) with 1/2 inch shank

Lots of clamps

Spindle sander is very very nice to have

Disk sander or belt sander is nice also

Starrett square

Digital calipers